Abstract
This paper gives a proposal for how order-sorted algebraic specification languages can be extended with higher-order functions. The approach taken is a generalisation to the order-sorted case of an approach given by Möller, Tarlecki and Wirsing for the many-sorted case. The main idea in the proposal is to only consider reachable extensional algebras. This leads to a very simple theory, where it is possible to relate the higher-order specifications to first order specifications.
The work described in this paper was carried out during a visit at Electrotechnical Laboratory in Tsukuba in Japan and was supported by Japan International Science and Technology Exchange Center. The production of the paper has been supported by the Danish Technical Research Council under the “Codesign” programme.
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References
H. Ehrig and B. Mahr. Fundamentals of Algebraic Specification 1, Equations and Initial Semantics. EATCS Monographs on Theoretical Computer Science, vol. 6. Springer-Verlag, 1985.
K. Futatsugi, J. Goguen, J. Jouannaud, and J. Meseguer. Principles of OBJ2. In 12th Symposium on POPL. Association for Computing Machinery, 1985.
J. Goguen and J. Meseguer. Order-Sorted Algebra I: Equational Deduction for Multiple Inheritance, Overloading, Exceptions and Partial Operations. Theoretical Computer Science, 105(2), 1992.
J. Goguen. Higher-Order Functions Considered Unnecessary for Higher Order Programming. Technical Report SRI-CSL-88-1R, SRI Int., 1988.
The RAISE Language Group. The RAISE Specification Language. The BCS Practitioners Series. Prentice Hall Int., 1992.
J. Goguen, T. Winkler, J. Meseguer, K. Futatsugi, and J. Jouannaud. Introducing OBJ. Technical Report SRI-CSL-92-03, SRI Int., 1992. Draft.
A. E. Haxthausen. Algebraic Specification with Higher-Order Functions. Technical Report ETL TR-94-18, Electrotechnical Laboratory, 1994.
B. Möller. Algebraic Specification with Higher-Order Operations. In IFIP TC2 Working Conference on Program Specification and Transformation. North-Holland, 1986.
N. Marti-Oliet and J. Meseguer. Inclusions and Subtypes. Technical Report SRI-CSL-90-16, SRI Int., 1990.
B. Möller, A. Tarlecki, and M. Wirsing. Algebraic Specification of Reachable Higher-Order Algebras. In 5th workshop on Specification of Abstract Datatypes, number 332 in LNCS. Springer-Verlag, 1988.
B. Möller, A. Tarlecki, and M. Wirsing. Algebraic Specifications with Built-in Domain Constructions. In CAAP'88, number 299 in LNCS. Springer-Verlag, 1988.
A. Poigné. On Specifications, Theories and Models with Higher Types. Information and Control, 68, 1986.
Z. Qian. Relation-sorted algebraic specifications with built-in coercers: Parameterization and parameter passing. In Categorical Methods in Computer Science, number 393 in LNCS. Springer-Verlag, 1989.
Z. Qian. Higher-Order Order-Sorted Algebras. In Algebraic and Logic Programming, number 463 in LNCS. Springer-Verlag, 1990.
J. Reynolds. Using category theory to design implicit conversions and generic operators. In Semantics-Directed Compiler Generation, number 94 in LNCS. Springer-Verlag, 1980.
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Haxthausen, A.E. (1995). Order-sorted algebraic specifications with higher-order functions. In: Alagar, V.S., Nivat, M. (eds) Algebraic Methodology and Software Technology. AMAST 1995. Lecture Notes in Computer Science, vol 936. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60043-4_50
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DOI: https://doi.org/10.1007/3-540-60043-4_50
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